A rectangle ABCD, where A≡$$0$$,$$0$$, B≡$$4$$,$$0$$, C≡$$4$$,$$2$$, D≡$$0$$,$$2$$, undergoes the following transformation successively :i. $$f1x$$,y→y,xii. $$f2x$$,y→$$x+3y$$,yiii. $$f3x$$,y→x−$$y/2$$,$$(x+y/2)The$$ final figure will be

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A rectangle ABCD, where A≡$$0$$,$$0$$, B≡$$4$$,$$0$$, C≡$$4$$,$$2$$, D≡$$0$$,$$2$$, undergoes the following transformation successively :i. $$f1x$$,y→y,xii. $$f2x$$,y→$$x+3y$$,yiii. $$f3x$$,y→x−$$y/2$$,$$(x+y/2)The$$ final figure will be

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Clearly, A will remains as $$0$$,$$0$$; $$f1will$$ make B $$as(0$$, $$4)$$ $$f2$$ will make it $$12$$,$$4$$, and $$f3$$ will make it (4$$, $$8) $$f1$$ will make C as $$2$$,$$4$$,$$f2$$ will make it $$14$$,$$4$$, and $$f3$$ will make it $$5$$,$$9$$. Finally, $$f1$$ will make D as $$2$$,$$0$$,$$f2will$$ make it $$2$$,$$0$$ and $$f3$$ will make it $$1$$,$$1$$. So, we finally get A≡$$0$$,$$0$$, B≡$$4$$,$$8$$, C≡$$5$$,$$9$$ and D≡$$1$$,$$1$$. Hence,$$mAB=84$$, $$mBC=9$$−$$85$$−$$4=1$$, $$mCD=9$$−$$15$$−$$1=84mAD=1$$, $$mAC=95$$,$$mBD=8$$−$$14$$−$$1=73Hence$$, the final figure will be a parallelogram

A rectangle ABCD, where A≡0,0, B≡4,0, C≡4,2, D≡0,2, undergoes the following transformation successively :i. f1x,y→y,xii. f2x,y→x+3y,yiii. f3x,y→x−y/2,(x+y/2)The final figure will be

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